# ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that AO/BO = CO/DO

**Solution:**

As we know If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

In trapezium ABCD

AB||CD, AC, and BD intersect at ‘O’

Construct XY parallel to AB and CD (XY||AB, XY||CD) through ‘O’

In ΔABC

OY || AB (construction)

According to theorem 6.1 (Basic Proportionality Theorem)

BY/CY = AO/OC................. (I)

In ΔBCD

OY || CD (construction)

According to theorem 6.1 (Basic Proportionality Theorem)

BY/CY = OB/OD................. (II)

From (I) and (II)

OA/OC = OB/ OD

⇒ OA/OB = OC/OD

**Video Solution:**

## ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that AO/BO = CO/DO

### Class 10 Maths NCERT Solutions - Chapter 6 Exercise 6.2 Question 9:

ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that AO/BO = CO/DO

Hence it is proved that AO/BO = CO/DO if ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O